Equation

Standard Description

Velocity Field Description

cl. vac. feq.

$\Delta V=0$

$v\left[\text{div}\left(v\right)\right]+\text{div}\left(v\mathrm{,}v\right)=0$

rel. vac. feq.

$\text{Ric}\left(v\mathrm{,}w\right)=0$

$u\left[\text{div}\left(u\right)\right]+\text{div}\left(u\mathrm{,}u\right)=0$

cl. mat. feq.

$\Delta V=4\pi \rho$

$v\left[\text{div}\left(v\right)\right]+\text{div}\left(v\mathrm{,}v\right)=-4\pi \rho$

rel. mat. feq. (free part.)

$\text{Ric}-\left(R/2\right)g=8\pi T$

$w\left[\text{div}\left(w\right)\right]+\text{div}\left(w\mathrm{,}w\right)=-4\pi \rho$ for $w=u$ , $u_{\perp }$ , $\left(u+u_{\perp }\right)/\sqrt{2}$